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"Although if no one understands the frontier math (because no one is getting paid to), I'm not sure it even matters what the quality of the cpu math is?"

Presumably AI will be connect the dots to the applications. As the declaration says, this isn't just about math. Human understanding is losing economic value. You can understand stuff on your own time, I guess.

The standard justification for pure math to holders of purse-strings is something like "it might lead to a useful application down the road, like crypto, who knows". That looks pretty inefficient now. We have to entertain the possibility that AI can develop the math needed for any application we put to it. Eg if number theory didn't exist, we could have asked AI for a way to transit messages securely and it would maybe come up with fermats little theorem as part of its solution or maybe come up with an approach we can't conceive of right now seeing as most of us are constrained to available number theory. Like how in the last year when I give an LLM a programming project I see it doesnt even bother with of the many software libraries I and others have written and just codes up the calls it needs on the fly or finds some other ad hoc solution.

> It's a bit like a tree falling in a forest. If an LLM proves a theorem but no one understands it, did it make a sound?

But in future most proofs will be for consumption by other AI models in the pursuit of yet other proofs.

It's kind of surprising so many mathematicians act surprised by this given this was clearly where automated proof assistants would lead. I guess they assumed they'd always be the ones guiding them.

> But in future most proofs will be for consumption by other AI models in the pursuit of yet other proofs.

What is the purpose of that?

Its like art being produced for AI to consume. What is gained from that?

Well if it proves useless presumably they'd stop doing it.

But if AI is to recursively self improve understanding and evolving its own foundations, which are clearly mathematical, is essential. There is no need for humans to grasp what is going on in that loop.

Math also has applications, and they don't rely on human mathematicians doing the math.

I mean, was the point of math ever just because some humans enjoyed doing it? Even though a lot of it is theoretical, there's been all sorts of useful things that have come out of it as well due to an improved understanding of the universe through new ways of thinking about it. If it got to the point where no human could understand it and there were no ways to actually use it, I don't think anyone would bother having their computers doing it at all.

wouldn't AI solving problems in science, engineering, economics, etc be able to apply the new AI math?

Yeah, that's kind of my point. I would have to imagine that the people investing in AI doing math (using "investing" loosely, not just financial but hardware/energy/opportunity cost as well, which may or may not seem roughly equivalent to money depending on your viewpoint) would just stop unless it remained possible to apply in some way or was understandable by humans.

> was the point of math ever just because some humans enjoyed doing it?

Yes.

Friends and I often work on Putnam problems and this series:

The (Almost) Impossible Integrals, Sums, and Series by Cornel Ioan Vălean

You can enjoy math, but that was never the only reason people in general did math. (It was the only reason for some people, sure.)

Your claim confuses me. This history of math is replete with people doing it for the love of the game.

As I said, these people exist. And math is fun!

But it's far from the only reason people in general do and have done math.

What would stop you from doing that if AI happened to be doing a bunch of different or more advanced stuff? I assume that the fact that there are humans doing other or more advanced stuff doesn't dissuade you from doing it for fun?

It's going to be hard to compete with something that has access to all of math at once and can find connections between elements that appear unrelated to humans.

And at some point AI will start suggesting - or doing - physical experiments.

Presumably some of the proofs will have applications beneficial to humans beyond impressing other mathematicians, and AI will surface them, or use them directly.

I would argue people getting paid to play chess was a short lived phenomenon anyway if you put it in context. The transition there is less related to the introduction of chess engines and more related to the shift in the media landscape.

When there's a billion people playing something, money will never be an issue for those at the top. Even things like chess.com was able to sponsor a tournament with a million dollar prize pool.

Also I'd argue that chess's utility is ultimately the same as pure math, particularly in esoteric fields. These things are highly unlikely to ever lead to any sort of real world breakthrough or application. The main benefit is an outlet for human logic, creativity, and exploration - which significant self improvement possible along the journey for players.

Though I think even that's probably too socially utilitarian. I think ultimately the 'real' drive is the same in both fields - it's fun and personally rewarding.

> Though I think even that's probably too socially utilitarian. I think ultimately the 'real' drive is the same in both fields - it's fun and personally rewarding.

That's fine, and no amount of machine excellence will keep you from enjoying recreational chess or recreational math.

Ah but it's enjoyable for billionaire and pauper alike. And the former tends to enjoy sponsoring it for the sake of seeing and promoting the bounds of human capability.

Mathematics is more than establishing arbitrary facts (although some look like curiosities), it's also defining what interesting research directions are and establishing common language/notation. I think that will stay relevant?

People become interested in things when they become invested in it personally, because they've contributed to it. So I don't think it will stay relevant...

In theory you can automate finding interesting research directions by identifying conjectures with many dependencies. And notation has never been mathematicians' forte, with them trying to cram the entirety of universe into single letters.

Why? How do you define interesting research directions? That used to be defined by testing the limits of human understanding i.e. some people can't figure something out. AI might have very different ideas about what is interesting and I am not sure what humans would get out of putting years into understanding AI proofs for what? What are we doing at that point? Like if you spend years understanding some AI proof of theorem 123456, why is that meaningful? I am actually asking why you think defining interesting research directions will stay relevant. In my opinion, people spend years acquiring knowledge so they can work on problems which is separate.

There's two points about this I am assuming 1) Mathematics actually has a significant subjectivity to it and is community oriented and not just climbing a never ending list of theorems that exists in the universe 2) A lot of mathematical research work is inside of a subfield and isn't directly motivated by applications. Sometimes it is but e.g. people don't work on obscure theorems about elliptic curves because of a dire need for that but more because the community found it interesting.

>but no one understands it, did it make a sound?

Does your "one" only contain humans or does it also contain other AI systems. AI math is not a single monolithic thing, but a distributed one. I see value in sharing proofs even among just AI.